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Simplifying 49x2 + -125x + -450 = 0 Reorder the terms: -450 + -125x + 49x2 = 0 Solving -450 + -125x + 49x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 49 the coefficient of the squared term: Divide each side by '49'. -9.183673469 + -2.551020408x + x2 = 0 Move the constant term to the right: Add '9.183673469' to each side of the equation. -9.183673469 + -2.551020408x + 9.183673469 + x2 = 0 + 9.183673469 Reorder the terms: -9.183673469 + 9.183673469 + -2.551020408x + x2 = 0 + 9.183673469 Combine like terms: -9.183673469 + 9.183673469 = 0.000000000 0.000000000 + -2.551020408x + x2 = 0 + 9.183673469 -2.551020408x + x2 = 0 + 9.183673469 Combine like terms: 0 + 9.183673469 = 9.183673469 -2.551020408x + x2 = 9.183673469 The x term is -2.551020408x. Take half its coefficient (-1.275510204). Square it (1.626926281) and add it to both sides. Add '1.626926281' to each side of the equation. -2.551020408x + 1.626926281 + x2 = 9.183673469 + 1.626926281 Reorder the terms: 1.626926281 + -2.551020408x + x2 = 9.183673469 + 1.626926281 Combine like terms: 9.183673469 + 1.626926281 = 10.81059975 1.626926281 + -2.551020408x + x2 = 10.81059975 Factor a perfect square on the left side: (x + -1.275510204)(x + -1.275510204) = 10.81059975 Calculate the square root of the right side: 3.28794765 Break this problem into two subproblems by setting (x + -1.275510204) equal to 3.28794765 and -3.28794765.Subproblem 1
x + -1.275510204 = 3.28794765 Simplifying x + -1.275510204 = 3.28794765 Reorder the terms: -1.275510204 + x = 3.28794765 Solving -1.275510204 + x = 3.28794765 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.275510204' to each side of the equation. -1.275510204 + 1.275510204 + x = 3.28794765 + 1.275510204 Combine like terms: -1.275510204 + 1.275510204 = 0.000000000 0.000000000 + x = 3.28794765 + 1.275510204 x = 3.28794765 + 1.275510204 Combine like terms: 3.28794765 + 1.275510204 = 4.563457854 x = 4.563457854 Simplifying x = 4.563457854Subproblem 2
x + -1.275510204 = -3.28794765 Simplifying x + -1.275510204 = -3.28794765 Reorder the terms: -1.275510204 + x = -3.28794765 Solving -1.275510204 + x = -3.28794765 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.275510204' to each side of the equation. -1.275510204 + 1.275510204 + x = -3.28794765 + 1.275510204 Combine like terms: -1.275510204 + 1.275510204 = 0.000000000 0.000000000 + x = -3.28794765 + 1.275510204 x = -3.28794765 + 1.275510204 Combine like terms: -3.28794765 + 1.275510204 = -2.012437446 x = -2.012437446 Simplifying x = -2.012437446Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.563457854, -2.012437446}
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